From 2b1813563ff7cb94fa1c9811bf8dd93a8b39be23 Mon Sep 17 00:00:00 2001
From: Neil Smith <neil.git@njae.me.uk>
Date: Tue, 25 Jul 2017 11:06:08 +0100
Subject: [PATCH] Updated file name

---
 08-word-chains/explore-word-chain-4.ipynb | 510 ++++++++++++++--------
 1 file changed, 320 insertions(+), 190 deletions(-)

diff --git a/08-word-chains/explore-word-chain-4.ipynb b/08-word-chains/explore-word-chain-4.ipynb
index 2c9faf7..d16966d 100644
--- a/08-word-chains/explore-word-chain-4.ipynb
+++ b/08-word-chains/explore-word-chain-4.ipynb
@@ -2,7 +2,7 @@
  "cells": [
   {
    "cell_type": "code",
-   "execution_count": 4,
+   "execution_count": 1,
    "metadata": {
     "collapsed": true
    },
@@ -16,7 +16,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 5,
+   "execution_count": 3,
    "metadata": {},
    "outputs": [
     {
@@ -25,19 +25,19 @@
        "2336"
       ]
      },
-     "execution_count": 5,
+     "execution_count": 3,
      "metadata": {},
      "output_type": "execute_result"
     }
    ],
    "source": [
-    "words = [w.strip() for w in open('08-offices.txt').readlines()]\n",
+    "words = [w.strip() for w in open('08-rooms.txt').readlines()]\n",
     "len(words)"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 6,
+   "execution_count": 4,
    "metadata": {},
    "outputs": [
     {
@@ -55,7 +55,7 @@
        " 'achy']"
       ]
      },
-     "execution_count": 6,
+     "execution_count": 4,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -66,7 +66,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 7,
+   "execution_count": 5,
    "metadata": {
     "collapsed": true
    },
@@ -83,7 +83,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 8,
+   "execution_count": 6,
    "metadata": {
     "collapsed": true
    },
@@ -98,7 +98,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 9,
+   "execution_count": 7,
    "metadata": {
     "collapsed": true
    },
@@ -110,7 +110,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 10,
+   "execution_count": 8,
    "metadata": {},
    "outputs": [
     {
@@ -119,7 +119,7 @@
        "['able']"
       ]
      },
-     "execution_count": 10,
+     "execution_count": 8,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -130,7 +130,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 11,
+   "execution_count": 9,
    "metadata": {},
    "outputs": [
     {
@@ -139,7 +139,7 @@
        "['axle', 'abbe', 'ably']"
       ]
      },
-     "execution_count": 11,
+     "execution_count": 9,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -150,7 +150,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 12,
+   "execution_count": 10,
    "metadata": {
     "collapsed": true
    },
@@ -163,7 +163,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 13,
+   "execution_count": 11,
    "metadata": {},
    "outputs": [
     {
@@ -172,7 +172,7 @@
        "0"
       ]
      },
-     "execution_count": 13,
+     "execution_count": 11,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -183,7 +183,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 14,
+   "execution_count": 12,
    "metadata": {
     "collapsed": true
    },
@@ -200,7 +200,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 15,
+   "execution_count": 13,
    "metadata": {},
    "outputs": [
     {
@@ -209,7 +209,7 @@
        "[['abbe', 'able']]"
       ]
      },
-     "execution_count": 15,
+     "execution_count": 13,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -220,7 +220,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 16,
+   "execution_count": 14,
    "metadata": {},
    "outputs": [
     {
@@ -229,7 +229,7 @@
        "[['abbe', 'able', 'axle'], ['abbe', 'able', 'ably']]"
       ]
      },
-     "execution_count": 16,
+     "execution_count": 14,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -240,7 +240,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 17,
+   "execution_count": 15,
    "metadata": {},
    "outputs": [
     {
@@ -249,7 +249,7 @@
        "[['abbe', 'able', 'ably', 'ally']]"
       ]
      },
-     "execution_count": 17,
+     "execution_count": 15,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -260,7 +260,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 18,
+   "execution_count": 16,
    "metadata": {
     "collapsed": true
    },
@@ -286,7 +286,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 19,
+   "execution_count": 17,
    "metadata": {
     "collapsed": true
    },
@@ -314,7 +314,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 20,
+   "execution_count": 18,
    "metadata": {},
    "outputs": [
     {
@@ -334,7 +334,7 @@
        "['abbe', 'able', 'ably', 'ally']"
       ]
      },
-     "execution_count": 20,
+     "execution_count": 18,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -345,7 +345,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 21,
+   "execution_count": 19,
    "metadata": {
     "collapsed": true
    },
@@ -371,7 +371,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 22,
+   "execution_count": 20,
    "metadata": {},
    "outputs": [
     {
@@ -391,7 +391,7 @@
        "['abbe', 'able', 'ably', 'ally']"
       ]
      },
-     "execution_count": 22,
+     "execution_count": 20,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -402,7 +402,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 23,
+   "execution_count": 21,
    "metadata": {},
    "outputs": [
     {
@@ -1091,7 +1091,13 @@
       "['cart', 'part', 'park', 'pars']\n",
       "['cart', 'part', 'pars', 'bars']\n",
       "['cart', 'part', 'pars', 'cars']\n",
-      "['cart', 'part', 'pars', 'ears']\n",
+      "['cart', 'part', 'pars', 'ears']\n"
+     ]
+    },
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
       "['cart', 'part', 'pars', 'jars']\n",
       "['cart', 'part', 'pars', 'mars']\n",
       "['cart', 'part', 'pars', 'oars']\n",
@@ -1545,7 +1551,7 @@
        "['cart', 'cant', 'cans', 'vans']"
       ]
      },
-     "execution_count": 23,
+     "execution_count": 21,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1556,7 +1562,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 24,
+   "execution_count": 22,
    "metadata": {},
    "outputs": [
     {
@@ -1565,7 +1571,7 @@
        "['cart', 'cant', 'cane', 'vane']"
       ]
      },
-     "execution_count": 24,
+     "execution_count": 22,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -1576,7 +1582,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 25,
+   "execution_count": 23,
    "metadata": {},
    "outputs": [
     {
@@ -2162,7 +2168,7 @@
        " 'vane']"
       ]
      },
-     "execution_count": 25,
+     "execution_count": 23,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2173,7 +2179,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 26,
+   "execution_count": 24,
    "metadata": {
     "collapsed": true
    },
@@ -2201,7 +2207,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 27,
+   "execution_count": 25,
    "metadata": {},
    "outputs": [
     {
@@ -2220,7 +2226,7 @@
        "['cart', 'cant', 'cane', 'vane']"
       ]
      },
-     "execution_count": 27,
+     "execution_count": 25,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2231,7 +2237,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 28,
+   "execution_count": 26,
    "metadata": {
     "collapsed": true
    },
@@ -2261,7 +2267,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 29,
+   "execution_count": 27,
    "metadata": {},
    "outputs": [
     {
@@ -2280,7 +2286,7 @@
        "['cart', 'cant', 'cane', 'vane']"
       ]
      },
-     "execution_count": 29,
+     "execution_count": 27,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2300,7 +2306,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 30,
+   "execution_count": 28,
    "metadata": {},
    "outputs": [
     {
@@ -2309,7 +2315,7 @@
        "94"
       ]
      },
-     "execution_count": 30,
+     "execution_count": 28,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2335,7 +2341,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 31,
+   "execution_count": 29,
    "metadata": {},
    "outputs": [
     {
@@ -2344,7 +2350,7 @@
        "2204"
       ]
      },
-     "execution_count": 31,
+     "execution_count": 29,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2355,7 +2361,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 32,
+   "execution_count": 30,
    "metadata": {},
    "outputs": [
     {
@@ -2364,7 +2370,7 @@
        "1"
       ]
      },
-     "execution_count": 32,
+     "execution_count": 30,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2375,7 +2381,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 33,
+   "execution_count": 31,
    "metadata": {
     "scrolled": true
    },
@@ -2386,7 +2392,7 @@
        "Counter({1: 75, 2: 6, 3: 7, 4: 2, 5: 2, 6: 1, 2204: 1})"
       ]
      },
-     "execution_count": 33,
+     "execution_count": 31,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2397,7 +2403,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 34,
+   "execution_count": 32,
    "metadata": {},
    "outputs": [
     {
@@ -2406,7 +2412,7 @@
        "[5]"
       ]
      },
-     "execution_count": 34,
+     "execution_count": 32,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2417,7 +2423,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 35,
+   "execution_count": 33,
    "metadata": {},
    "outputs": [
     {
@@ -2426,7 +2432,7 @@
        "[{'abbe', 'able', 'ably', 'ally', 'axle'}]"
       ]
      },
-     "execution_count": 35,
+     "execution_count": 33,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2437,7 +2443,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 36,
+   "execution_count": 34,
    "metadata": {},
    "outputs": [
     {
@@ -2446,7 +2452,7 @@
        "['buns', 'bunk', 'punk']"
       ]
      },
-     "execution_count": 36,
+     "execution_count": 34,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2457,7 +2463,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 37,
+   "execution_count": 35,
    "metadata": {
     "collapsed": true
    },
@@ -2472,7 +2478,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 38,
+   "execution_count": 36,
    "metadata": {
     "collapsed": true
    },
@@ -2495,7 +2501,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 39,
+   "execution_count": 37,
    "metadata": {
     "collapsed": true
    },
@@ -2506,33 +2512,33 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 40,
+   "execution_count": 38,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "['bops', 'bogs', 'begs', 'bees', 'byes', 'eyes', 'eyed']\n",
-      "['foal', 'foil', 'fail']\n",
-      "['bush', 'bash', 'base', 'bale', 'ball', 'boll']\n",
-      "['rift', 'lift', 'life', 'live', 'give', 'gave']\n",
-      "['club', 'clue', 'flue', 'flee', 'fled', 'pled', 'pied', 'lied', 'lien', 'mien']\n",
-      "['rung', 'dung', 'ding', 'dins', 'dies', 'lies', 'lien']\n",
-      "['baas', 'bags', 'bugs', 'bums', 'sums', 'sumo']\n",
-      "['fits', 'bits', 'bins', 'bind']\n",
-      "['lids', 'bids', 'bias', 'boas', 'boat', 'boot', 'soot', 'snot', 'snob']\n",
-      "['cake', 'came', 'cams', 'caws', 'cows', 'tows']\n",
-      "['tort', 'toot', 'trot', 'troy', 'tray', 'tram', 'cram']\n",
-      "['sews', 'pews', 'pees', 'peed', 'pied']\n",
-      "['lack', 'hack', 'hawk', 'haws', 'hows', 'tows']\n",
-      "['dots', 'dons', 'dens', 'dent', 'pent', 'pest', 'peso']\n",
-      "['ekes', 'eyes', 'byes', 'bees', 'beet', 'bent', 'lent', 'lept']\n",
-      "['ruin', 'rain', 'gain', 'grin', 'grid', 'arid', 'acid', 'aced', 'iced']\n",
-      "['sing', 'sins', 'bins', 'bias', 'bras', 'bray', 'tray', 'trap']\n",
-      "['lira', 'lire', 'wire', 'wise', 'wish']\n",
-      "['gash', 'cash', 'case', 'cape', 'rape']\n",
-      "['crop', 'coop', 'coot', 'loot', 'loft']\n"
+      "['drip', 'grip', 'grit', 'gait', 'bait', 'bast', 'base', 'babe']\n",
+      "['cape', 'cope', 'dope', 'dole', 'dolt']\n",
+      "['laze', 'late', 'lats', 'pats']\n",
+      "['zest', 'best', 'bust', 'buss', 'buds', 'suds']\n",
+      "['gape', 'gaps', 'paps', 'peps', 'pees', 'peel']\n",
+      "['yogi', 'yoga', 'toga', 'togs', 'tors', 'tore']\n",
+      "['flux', 'flex', 'fled', 'feed', 'fees', 'foes', 'toes', 'toys']\n",
+      "['bike', 'bake', 'base', 'bast', 'best', 'beet', 'feet']\n",
+      "['tows', 'lows', 'laws', 'lams', 'lame']\n",
+      "['jock', 'pock', 'pork', 'pore', 'pure']\n",
+      "['tabu', 'tabs', 'cabs', 'caws', 'cows', 'cowl', 'coil', 'coif']\n",
+      "['reek', 'week', 'wees', 'weds', 'wads', 'wadi']\n",
+      "['gene', 'gone', 'gong', 'song']\n",
+      "['mete', 'mate', 'bate', 'bats', 'baas', 'bras', 'brag', 'crag', 'cram']\n",
+      "['gnus', 'anus', 'ants', 'acts', 'aces', 'ayes', 'byes', 'bees', 'been', 'teen']\n",
+      "['comb', 'come', 'core', 'corn', 'torn', 'tern']\n",
+      "['ouch', 'much', 'muck', 'buck', 'beck', 'beak', 'beat', 'teat', 'that', 'than', 'khan']\n",
+      "['rids', 'reds', 'reps', 'peps', 'peas', 'peal', 'deal']\n",
+      "['calm', 'balm', 'bald', 'bold', 'bolt', 'bout', 'tout']\n",
+      "['toed', 'toad', 'goad', 'grad', 'gray', 'grey', 'grew']\n"
      ]
     }
    ],
@@ -2544,7 +2550,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 41,
+   "execution_count": 39,
    "metadata": {},
    "outputs": [
     {
@@ -2553,7 +2559,7 @@
        "['cops', 'coos', 'coon', 'coin', 'chin', 'thin', 'this', 'thus', 'thug']"
       ]
      },
-     "execution_count": 41,
+     "execution_count": 39,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2564,7 +2570,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 42,
+   "execution_count": 40,
    "metadata": {},
    "outputs": [
     {
@@ -2573,7 +2579,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 42,
+     "execution_count": 40,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2584,7 +2590,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 73,
+   "execution_count": 41,
    "metadata": {},
    "outputs": [
     {
@@ -2593,7 +2599,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 73,
+     "execution_count": 41,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2604,7 +2610,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 43,
+   "execution_count": 42,
    "metadata": {},
    "outputs": [
     {
@@ -2613,7 +2619,7 @@
        "['hate', 'have', 'hove', 'love']"
       ]
      },
-     "execution_count": 43,
+     "execution_count": 42,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2624,7 +2630,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 44,
+   "execution_count": 43,
    "metadata": {},
    "outputs": [
     {
@@ -2633,7 +2639,7 @@
        "['wars', 'ware', 'wave', 'wove', 'love']"
       ]
      },
-     "execution_count": 44,
+     "execution_count": 43,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2644,7 +2650,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 45,
+   "execution_count": 44,
    "metadata": {},
    "outputs": [
     {
@@ -2652,7 +2658,7 @@
      "output_type": "stream",
      "text": [
       "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 850 µs\n"
+      "Wall time: 212 µs\n"
      ]
     },
     {
@@ -2661,7 +2667,7 @@
        "5"
       ]
      },
-     "execution_count": 45,
+     "execution_count": 44,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2672,7 +2678,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 46,
+   "execution_count": 45,
    "metadata": {},
    "outputs": [
     {
@@ -2680,7 +2686,7 @@
      "output_type": "stream",
      "text": [
       "CPU times: user 0 ns, sys: 0 ns, total: 0 ns\n",
-      "Wall time: 353 µs\n"
+      "Wall time: 203 µs\n"
      ]
     },
     {
@@ -2689,7 +2695,7 @@
        "5"
       ]
      },
-     "execution_count": 46,
+     "execution_count": 45,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2700,15 +2706,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 47,
+   "execution_count": 46,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 76 ms, sys: 0 ns, total: 76 ms\n",
-      "Wall time: 75.1 ms\n"
+      "CPU times: user 24 ms, sys: 0 ns, total: 24 ms\n",
+      "Wall time: 23.2 ms\n"
      ]
     },
     {
@@ -2717,7 +2723,7 @@
        "404"
       ]
      },
-     "execution_count": 47,
+     "execution_count": 46,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2728,8 +2734,10 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
-   "metadata": {},
+   "execution_count": 47,
+   "metadata": {
+    "collapsed": true
+   },
    "outputs": [],
    "source": [
     "# %time len(bfs_search('wars', 'love'))"
@@ -2737,16 +2745,35 @@
   },
   {
    "cell_type": "code",
-   "execution_count": null,
+   "execution_count": 48,
    "metadata": {},
-   "outputs": [],
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "CPU times: user 332 ms, sys: 0 ns, total: 332 ms\n",
+      "Wall time: 331 ms\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "5"
+      ]
+     },
+     "execution_count": 48,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
    "source": [
     "%time len(bfs_search_closed('wars', 'love'))"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 50,
+   "execution_count": 49,
    "metadata": {},
    "outputs": [
     {
@@ -2755,7 +2782,7 @@
        "['fear', 'feat', 'fest', 'lest', 'lost', 'lose', 'love']"
       ]
      },
-     "execution_count": 50,
+     "execution_count": 49,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2766,7 +2793,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 51,
+   "execution_count": 50,
    "metadata": {},
    "outputs": [
     {
@@ -2775,7 +2802,7 @@
        "['fail', 'fall', 'pall', 'pals', 'pass']"
       ]
      },
-     "execution_count": 51,
+     "execution_count": 50,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2786,7 +2813,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 52,
+   "execution_count": 51,
    "metadata": {},
    "outputs": [
     {
@@ -2795,7 +2822,7 @@
        "['star', 'soar', 'boar', 'boor', 'boon', 'born']"
       ]
      },
-     "execution_count": 52,
+     "execution_count": 51,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2806,7 +2833,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 53,
+   "execution_count": 52,
    "metadata": {},
    "outputs": [
     {
@@ -2825,7 +2852,7 @@
        " 'pass']"
       ]
      },
-     "execution_count": 53,
+     "execution_count": 52,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2836,7 +2863,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 54,
+   "execution_count": 53,
    "metadata": {},
    "outputs": [
     {
@@ -2858,7 +2885,7 @@
        " 'past']"
       ]
      },
-     "execution_count": 54,
+     "execution_count": 53,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2869,7 +2896,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 55,
+   "execution_count": 54,
    "metadata": {},
    "outputs": [
     {
@@ -2878,7 +2905,7 @@
        "[1]"
       ]
      },
-     "execution_count": 55,
+     "execution_count": 54,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2889,7 +2916,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 56,
+   "execution_count": 55,
    "metadata": {},
    "outputs": [
     {
@@ -2898,7 +2925,7 @@
        "[2204]"
       ]
      },
-     "execution_count": 56,
+     "execution_count": 55,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2909,14 +2936,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 57,
+   "execution_count": 56,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 12.3 s per loop\n"
+      "1 loop, best of 3: 8.08 s per loop\n"
      ]
     }
    ],
@@ -2927,14 +2954,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 58,
+   "execution_count": 57,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 200 ms per loop\n"
+      "10 loops, best of 3: 131 ms per loop\n"
      ]
     }
    ],
@@ -2945,7 +2972,7 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 59,
+   "execution_count": 58,
    "metadata": {},
    "outputs": [
     {
@@ -2963,7 +2990,7 @@
        " 'exit']"
       ]
      },
-     "execution_count": 59,
+     "execution_count": 58,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -2974,53 +3001,29 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 60,
+   "execution_count": 68,
    "metadata": {},
-   "outputs": [
-    {
-     "data": {
-      "text/plain": [
-       "{2: [['exes', 'exec'], ['rush', 'tush'], ['wile', 'wily'], ['shoo', 'shot']],\n",
-       " 3: [['bins', 'fink'], ['waft', 'wand'], ['heel', 'jell'], ['tent', 'west']],\n",
-       " 4: [['yore', 'polo'], ['hale', 'case'], ['horn', 'look'], ['tang', 'nuns']],\n",
-       " 5: [['crab', 'baas'], ['yens', 'dead'], ['work', 'paps'], ['tune', 'zaps']],\n",
-       " 6: [['mist', 'sold'], ['bats', 'sort'], ['leek', 'mads'], ['loop', 'dome']],\n",
-       " 7: [['rime', 'hoof'], ['grim', 'reed'], ['lies', 'eave'], ['ties', 'whiz']],\n",
-       " 8: [['drag', 'lied'], ['ages', 'yawl'], ['earl', 'deal'], ['gins', 'scab']],\n",
-       " 9: [['tyre', 'swum'], ['dike', 'flux'], ['hour', 'laze'], ['trek', 'bait']],\n",
-       " 10: [['ides', 'rasp'], ['egos', 'racy'], ['shim', 'ills'], ['bark', 'arty']],\n",
-       " 11: [['ergo', 'apex'], ['whey', 'owns'], ['anew', 'rapt'], ['thug', 'bate']],\n",
-       " 12: [['ream', 'imps'], ['meat', 'umps'], ['daze', 'knee'], ['clay', 'over']],\n",
-       " 13: [['oxen', 'blab'], ['blip', 'omen'], ['twig', 'ibis'], ['chew', 'umps']],\n",
-       " 14: [['amen', 'blip'], ['umps', 'futz'], ['amps', 'glib'], ['chum', 'whys']],\n",
-       " 15: [['thug', 'ibis']]}"
-      ]
-     },
-     "execution_count": 60,
-     "metadata": {},
-     "output_type": "execute_result"
-    }
-   ],
+   "outputs": [],
    "source": [
-    "solutions = {}\n",
-    "for _ in range(10000):\n",
-    "    start, goal = random.sample(bigset, 2)\n",
-    "    solution = astar_search_closed(start, goal)\n",
-    "    sl = len(solution)\n",
-    "    if sl not in solutions:\n",
-    "        solutions[sl] = []\n",
-    "    if len(solutions[sl]) < 4:\n",
-    "        solutions[sl].append([start, goal])\n",
+    "# solutions = {}\n",
+    "# for _ in range(10000):\n",
+    "#     start, goal = random.sample(bigset, 2)\n",
+    "#     solution = astar_search_closed(start, goal)\n",
+    "#     sl = len(solution)\n",
+    "#     if sl not in solutions:\n",
+    "#         solutions[sl] = []\n",
+    "#     if len(solutions[sl]) < 4:\n",
+    "#         solutions[sl].append([start, goal])\n",
     "        \n",
-    "#     if len(solution) >= 10:\n",
-    "#         solutions += [solution]\n",
+    "# #     if len(solution) >= 10:\n",
+    "# #         solutions += [solution]\n",
     "        \n",
-    "solutions"
+    "# solutions"
    ]
   },
   {
    "cell_type": "code",
-   "execution_count": 64,
+   "execution_count": 60,
    "metadata": {
     "collapsed": true
    },
@@ -3045,14 +3048,14 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 66,
+   "execution_count": 61,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "1 loop, best of 3: 487 ms per loop\n"
+      "1 loop, best of 3: 352 ms per loop\n"
      ]
     }
    ],
@@ -3063,15 +3066,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 67,
+   "execution_count": 62,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 768 ms, sys: 0 ns, total: 768 ms\n",
-      "Wall time: 768 ms\n"
+      "CPU times: user 452 ms, sys: 0 ns, total: 452 ms\n",
+      "Wall time: 449 ms\n"
      ]
     },
     {
@@ -3080,7 +3083,7 @@
        "14"
       ]
      },
-     "execution_count": 67,
+     "execution_count": 62,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3091,15 +3094,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 68,
+   "execution_count": 63,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 176 ms, sys: 0 ns, total: 176 ms\n",
-      "Wall time: 176 ms\n"
+      "CPU times: user 92 ms, sys: 0 ns, total: 92 ms\n",
+      "Wall time: 91.5 ms\n"
      ]
     },
     {
@@ -3108,7 +3111,7 @@
        "15"
       ]
      },
-     "execution_count": 68,
+     "execution_count": 63,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3119,15 +3122,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 69,
+   "execution_count": 64,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 72 ms, sys: 0 ns, total: 72 ms\n",
-      "Wall time: 70.6 ms\n"
+      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
+      "Wall time: 31.4 ms\n"
      ]
     },
     {
@@ -3136,7 +3139,7 @@
        "14"
       ]
      },
-     "execution_count": 69,
+     "execution_count": 64,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3147,15 +3150,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 70,
+   "execution_count": 65,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 32 ms, sys: 0 ns, total: 32 ms\n",
-      "Wall time: 35.7 ms\n"
+      "CPU times: user 16 ms, sys: 0 ns, total: 16 ms\n",
+      "Wall time: 17.2 ms\n"
      ]
     },
     {
@@ -3164,7 +3167,7 @@
        "14"
       ]
      },
-     "execution_count": 70,
+     "execution_count": 65,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3175,15 +3178,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 71,
+   "execution_count": 66,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 376 ms, sys: 4 ms, total: 380 ms\n",
-      "Wall time: 382 ms\n"
+      "CPU times: user 296 ms, sys: 4 ms, total: 300 ms\n",
+      "Wall time: 299 ms\n"
      ]
     },
     {
@@ -3192,7 +3195,7 @@
        "14"
       ]
      },
-     "execution_count": 71,
+     "execution_count": 66,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3203,15 +3206,15 @@
   },
   {
    "cell_type": "code",
-   "execution_count": 72,
+   "execution_count": 67,
    "metadata": {},
    "outputs": [
     {
      "name": "stdout",
      "output_type": "stream",
      "text": [
-      "CPU times: user 72 ms, sys: 4 ms, total: 76 ms\n",
-      "Wall time: 76.9 ms\n"
+      "CPU times: user 36 ms, sys: 0 ns, total: 36 ms\n",
+      "Wall time: 34.5 ms\n"
      ]
     },
     {
@@ -3220,7 +3223,7 @@
        "14"
       ]
      },
-     "execution_count": 72,
+     "execution_count": 67,
      "metadata": {},
      "output_type": "execute_result"
     }
@@ -3229,6 +3232,133 @@
     "%time len(astar_search_closed('imps', 'pros'))"
    ]
   },
+  {
+   "cell_type": "code",
+   "execution_count": 90,
+   "metadata": {},
+   "outputs": [
+    {
+     "name": "stdout",
+     "output_type": "stream",
+     "text": [
+      "bash bush True\n",
+      "rush bush True\n"
+     ]
+    },
+    {
+     "data": {
+      "text/plain": [
+       "2"
+      ]
+     },
+     "execution_count": 90,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "nb_count = collections.Counter()\n",
+    "for w in neighbours['rash']:\n",
+    "    for w2 in neighbours[w]:\n",
+    "        if w2 == 'bush': print(w, w2, w2 not in neighbours['rash'])\n",
+    "        if w2 != 'rash' and w2 not in neighbours['rash']:\n",
+    "            nb_count.update([w2])\n",
+    "nb_count.most_common(1)[0][1]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 91,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "['gush', 'hush', 'lush', 'mush', 'push', 'tush', 'bosh']"
+      ]
+     },
+     "execution_count": 91,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "[w for w in neighbours['bush'] if w in nb_count]"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 89,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "('gibe', 2)"
+      ]
+     },
+     "execution_count": 89,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "best_start = ''\n",
+    "best_overlap_count = 0\n",
+    "for w0 in neighbours:    \n",
+    "    nb_count = collections.Counter()\n",
+    "    for w in neighbours[w0]:\n",
+    "        for w2 in neighbours[w]:\n",
+    "            if w2 != w0 and w2 not in neighbours[w0]:\n",
+    "                nb_count.update([w2])\n",
+    "    if len(nb_count) > 0:\n",
+    "        if nb_count.most_common(1)[0][1] > best_overlap_count:\n",
+    "            best_start = w0\n",
+    "            best_overlap_count = nb_count.most_common(1)[0][1]\n",
+    "        \n",
+    "best_start, best_overlap_count"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 88,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "'memo'"
+      ]
+     },
+     "execution_count": 88,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "w0"
+   ]
+  },
+  {
+   "cell_type": "code",
+   "execution_count": 76,
+   "metadata": {},
+   "outputs": [
+    {
+     "data": {
+      "text/plain": [
+       "{'bash', 'rush'}"
+      ]
+     },
+     "execution_count": 76,
+     "metadata": {},
+     "output_type": "execute_result"
+    }
+   ],
+   "source": [
+    "set(neighbours['rash']) & set(neighbours['bush'])"
+   ]
+  },
   {
    "cell_type": "code",
    "execution_count": null,
-- 
2.34.1